FIT FOR A POWER KING: NRG Energy's David W. Crane (above) lives in this tony colonial mansion in Lawrenceville Township, NJ.Ben Parker

“Jack the Ripper’s” body count is now at least eight.

Three more sets of human remains were discovered yesterday on a mile-long stretch of remote beach where the Long Island serial killer’s five other presumed victims were found.

The grisly discoveries were made during “a very methodical, careful search” along Ocean Parkway between Gilgo and Oak beaches, said Suffolk Police Commissioner Richard Dormer.

He added that the search for more bodies will continue today.

The madman had remained under the radar — killing without attracting the attention of cops — for at least two years.

Then, in December, detectives began searching for Shannan Gilbert, a troubled hooker from Jersey City, who was last seen in Oak Beach in May 2010, running and pleading for help. Instead they found the bodies of four other prostitutes scattered in dense growth along the roadway.

The four hookers identified so far were all lured to Long Island by Craigslist ads, as was Gilbert.

The bodies of the four were all wrapped in burlap.

Dormer said the medical examiner will make it a priority to positively eliminate or identify Gilbert as one of the newly found remains. She is the only still-missing woman to whom police can put a name.

Twice before, her family was given reason to hope that her body had been found and that she could finally be laid to rest, only to be disappointed.

Gilbert, 24, had a metal pin in her upper body as a result of a prior surgery, and X-rays might help identify her quickly, sources said.

DNA samples have also been taken from her relatives.

The search yesterday was painstaking.

Using firetrucks with long ladders extended horizontally over the tangled brush, detectives from the special serial-killer task force found the remains by walking above the dense vegetation and peering down.

Cadaver dogs and a busload of police recruits also joined in the search.

Chief of Detectives Dominick Varrone said searching the tangled brambles was very difficult, even for the dogs.

Many cops have encountered poison ivy, and deer ticks have raised concern about Lyme disease. Of the new victims, Varrone would say only that their remains had been there for some time.

Even if no other bodies are found, the serial killer already is the second most prolific in Long Island’s history.

He has surpassed Robert Schulman’s total of five prostitutes, but not that of Joel Rifkin, who killed 17 hookers.

The victims of the latest serial killer who have been identified are:

* Amber Lynn Costello, 27, of North Babylon, who was last seen in her hometown last Sept. 2.

* Megan Waterman, 22, of Scarborough, Maine, last seen on Long Island June 6, 2010.

* Melissa Barthelmy, 24, reported missing from The Bronx on July 12, 2009.

* Maureen Brainard-Barnes, 25, of Norwich, Conn., last seen in Manhattan on July 9, 2007.

The fifth body, still unidentified, was discovered March 29.

Gilbert was last seen in May last year — fleeing from a john in the exclusive oceanfront community of Oak Beach, just a few miles from where the bodies have been found.

She cried out to a resident that “they’re trying to kill me.”

As soon as the resident picked up his phone to dial police, Gilbert fled and disappeared into the night.

Later, Gilbert called cops on her cellphone repeatedly over a 30-minute period.

She told them she thought she was on Jones Beach.

But police could not find her because she was actually on a beach several miles east.

Police cleared the local businessman who hired her to come to Long Island.